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Thermodynamic calculations
In principle, if the molecular geometry, energy, and vibrational frequencies are known, the thermodynamics properties (enthalpy, entropy, free energy) of the molecule can be calculated (Stull and Prophet, 1971). The results can be displayed using the Thermodynamic properties dialog, or viewed in the VAMP output file.

There is, however, a fundamental inconsistency inherent in the parameterization of semiempirical methods to reproduce heats of formation. The energy calculated by VAMP is the internal energy of a hypothetical motionless (Born-Oppenheimer) state. To relate this energy to heats of formation at 298 K, an atom-based scheme is used, assuming that the energy difference between the Born-Oppenheimer state and the molecule at 298 K can be treated in an additive fashion. This means that the zero-point energy and the energy required to warm the molecule to 298 K are assumed to be identical for isomers. This is clearly not the case and can lead to errors of up to 5 kcal mol-1.

A further problem arises in the calculation of the thermodynamic properties. As the methods are parameterized to reproduce the heat of formation at 298 K, this temperature must be used as the reference point for thermodynamics calculations. The calculation, however, gives an energy for a motionless molecule. This leads to a basic inconsistency. Thermodynamics calculations yield entropy, enthalpy, and free energy changes between the Born-Oppenheimer state and the temperature in question. The heat of formation scale must, however, be adjusted so that the value at 298 K is the same as that given in the normal calculation.

The result is that, in effect, we have to work with a fictitious Born-Oppenheimer energy in thermodynamics calculations. The best procedure is simply to ignore the "heat of formation" and to calculate thermodynamic quantities for reactions based on the Born-Oppenheimer energy and the calculated entropy and enthalpy changes, as for ab initio calculations.

Using the thermodynamic data
Once the enthalpy, entropy, and free energy of the molecule are calculated as a function of temperature, the results can be used to compute the heat of formation at any temperature. The heat of formation at 298 K is written to the VAMP output file and can be adjusted for different temperatures as follows:


Display the results using the Thermodynamic properties dialog or view them in the VAMP output file.
For the temperature of interest, say 100 K, compute the temperature-dependent contribution, enthalpy minus temperature times entropy (E - TS).
Compute E - TS at 298 K. If you did not compute the thermodynamics at exactly 298 K, pick the temperature closest to it (e.g., 300 K) or estimate it by interpolation.
Compute the difference in E - TS at the two temperatures and adjust the heat of formation at 298 K by that amount. For example, say that E - TS at 100 K is 0.5 kcal mol-1 and the value at 298 K is 2.2 kcal mol-1. You would compute the heat of formation at 100 K by subtracting 1.7 kcal mol-1 (2.2 - 0.5) from the heat of formation at 298 K given in the VAMP output file.

Further information
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wuchenwf(½ð±Ò+2,VIP+0):xiexie
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